Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int n, i, a[100000], l, k;
  cin >> n;
  for (i = 0; i < 100000; i++) {
    a[i] = ((i + 1) * (i + 2)) / 2;
    if (a[i] > 1000000000) break;
  }
  l = i - 1;
  for (i = 0; i < l; i++) {
    k = n - a[i];
    if (k > 0) {
      if (binary_search(a, a + l, k)) {
        cout << "YES";
        return 0;
      }
    } else
      break;
  }
  cout << "NO";
  return 0;
}